Random rotation on child particles?
The "Random rough" parameter of the children seems the only one that affects individual children without too much correlation between them¹. Unfortunately though, it inevitably affects sizes too. Also, it can't be constrained to the normal axis (in case you needed it):



3 hair particles, 4 children each

A real "random rotation" doesn't exist for children specifically.

¹ (if "Size" is small enough)